Differential Effect of Delays and Network Topology on Temporal Pattern Formation

TL;DR

This paper studies how different types of transmission delays affect the temporal ordering in networks of Rössler oscillators with small-world topology, revealing contrasting effects of delay types on network order.

Contribution

It introduces and compares the effects of length independent and length dependent delays on temporal pattern formation in oscillator networks with SWN topology.

Findings

Length independent delays increase temporal order.

Length dependent delays disrupt local order.

Delays significantly alter network dynamics.

Abstract

We investigate the effects of transmission delays on the formation of temporally ordered states in networks of non-identical R\"ossler oscillators, having SWN topology. We show that incorporation of two different types of delay, length independent and length dependent, leads to dramatically different temporal properties of the network. In the first case formation of global random connections leads to increased temporal ordering, while in the second case it annihilates locally ordered clusters and forms a disordered state.